An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2
We describe the modulo $2$ de Rham-Witt complex of a field of characteristic $2$ , in terms of the powers of the augmentation ideal of the $\mathbb {Z}/2$ -geometric fixed points of real topological restriction homology ${\mathrm {TRR}}$ . This is analogous to the conjecture...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000404/type/journal_article |
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| Summary: | We describe the modulo
$2$
de Rham-Witt complex of a field of characteristic
$2$
, in terms of the powers of the augmentation ideal of the
$\mathbb {Z}/2$
-geometric fixed points of real topological restriction homology
${\mathrm {TRR}}$
. This is analogous to the conjecture of Milnor, proved in [Kat82] for fields of characteristic
$2$
, which describes the modulo
$2$
Milnor K-theory in terms of the powers of the augmentation ideal of the Witt group of symmetric forms. Our proof provides a somewhat explicit description of these objects, as well as a calculation of the homotopy groups of the geometric fixed points of
${\mathrm {TRR}}$
and of real topological cyclic homology, for all fields. |
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| ISSN: | 2050-5094 |